Question: Multiply the following complex numbers: $({4+4i}) \cdot ({-2i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({4+4i}) \cdot ({-2i}) = $ $ ({4} \cdot {0}) + ({4} \cdot {-2}i) + ({4}i \cdot {0}) + ({4}i \cdot {-2}i) $ Then simplify the terms: $ (0) + (-8i) + (0i) + (-8 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 0 + (-8 + 0)i - 8i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 0 + (-8 + 0)i - (-8) $ The result is simplified: $ (0 + 8) + (-8i) = 8-8i $